메뉴 건너뛰기




Volumn 106, Issue 5-6, 2002, Pages 1197-1220

From the von Neumann equation to the quantum Boltzmann equation II: Identifying the born series

Author keywords

Density matrix; Fermi's Golden Rule; Low density limit; Oscillatory integrals; Time dependent scattering theory

Indexed keywords


EID: 0036102715     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1014098122698     Document Type: Article
Times cited : (18)

References (44)
  • 1
    • 0003930334 scopus 로고
    • Texts and Monographs in Physics (Springer-Verlag)
    • A. Bohm, Quantum Mechanics, Texts and Monographs in Physics (Springer-Verlag, 1979).
    • (1979) Quantum Mechanics
    • Bohm, A.1
  • 3
    • 0032326766 scopus 로고    scopus 로고
    • On the distribution of free path lengths for the periodic Lorentz gas
    • J. Bourgain, F. Golse, and B. Wennberg, On the distribution of free path lengths for the periodic Lorentz gas, Comm. Math. Phys. 190:491-508 (1998).
    • (1998) Comm. Math. Phys. , vol.190 , pp. 491-508
    • Bourgain, J.1    Golse, F.2    Wennberg, B.3
  • 5
    • 0141440452 scopus 로고    scopus 로고
    • University Paris 6
    • D. Calecki, Lecture (University Paris 6, 1997).
    • (1997) Lecture
    • Calecki, D.1
  • 6
    • 0035535173 scopus 로고    scopus 로고
    • From the von Neumann equation to the quantum Boltzmann equation in a deterministic framework
    • to appear in
    • F. Castella, From the von Neumann equation to the quantum Boltzmann equation in a deterministic framework, to appear in J. Stat. Phys. (2001).
    • (2001) J. Stat. Phys.
    • Castella, F.1
  • 8
    • 0038934841 scopus 로고    scopus 로고
    • On the derivation of a Quantum Boltzmann Equation from the periodic von Neumann equation
    • F. Castella, On the derivation of a Quantum Boltzmann Equation from the periodic von Neumann equation, Mod. Math. An. Num. 33:329-349 (1999).
    • (1999) Mod. Math. An. Num. , vol.33 , pp. 329-349
    • Castella, F.1
  • 9
    • 0033177365 scopus 로고    scopus 로고
    • Convergence de l'équation de von neumann vers l'équation de boltzmann quantique dans un cadre déterministe
    • F. Castella and P. Degond, Convergence de l'équation de von Neumann vers l'équation de Boltzmann Quantique dans un cadre déterministe, C. R. Acad. Sci. Sér. I 329:231-236 (1999).
    • (1999) C. R. Acad. Sci. Sér. I , vol.329 , pp. 231-236
    • Castella, F.1    Degond, P.2
  • 12
    • 0034338421 scopus 로고    scopus 로고
    • Fokker-Planck equations as scaling limits of reversible quantum systems
    • F. Castella, L. Erdös, F. Frommlet, and P. A. Markowich, Fokker-Planck equations as scaling limits of reversible quantum systems, J. Statist. Phys. 100:543-601 (2000).
    • (2000) J. Statist. Phys. , vol.100 , pp. 543-601
    • Castella, F.1    Erdös, L.2    Frommlet, F.3    Markowich, P.A.4
  • 15
    • 0041450241 scopus 로고
    • The low density limit for an N-level system interacting with a free Bose or Fermi gas
    • R. Dümcke, The low density limit for an N-level system interacting with a free Bose or Fermi gas, Comm. Math. Phys. 97:331-359 (1985).
    • (1985) Comm. Math. Phys. , vol.97 , pp. 331-359
    • Dümcke, R.1
  • 16
    • 0000632181 scopus 로고    scopus 로고
    • Linear boltzmann equation as scaling limit of quantum lorentz gas advances
    • (Atlanta, GA); Contemp. Math., (Amer. Math. Soc., Providence RI)
    • L. Erdös and H. T. Yau, Linear boltzmann equation as scaling limit of quantum lorentz gas advances, in Differential Equations and Mathematical Physics (Atlanta, GA, 1997), pp. 137-155; Contemp. Math., Vol. 217 (Amer. Math. Soc., Providence, RI, 1998).
    • (1997) Differential Equations and Mathematical Physics , vol.217 , pp. 137-155
    • Erdös, L.1    Yau, H.T.2
  • 17
    • 0034418177 scopus 로고    scopus 로고
    • Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation
    • L. Erdös and H. T. Yau, Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation, Comm. Pure Appl. Math. 53:667-735 (2000).
    • (2000) Comm. Pure Appl. Math. , vol.53 , pp. 667-735
    • Erdös, L.1    Yau, H.T.2
  • 18
    • 0031693941 scopus 로고    scopus 로고
    • Theory of electron transport in small semiconductor devices using the Pauli master equations
    • M. V. Fischetti, Theory of electron transport in small semiconductor devices using the Pauli master equations, J. Appl. Phys. 83:270-291 (1998).
    • (1998) J. Appl. Phys. , vol.83 , pp. 270-291
    • Fischetti, M.V.1
  • 19
    • 0000111115 scopus 로고
    • On the weak coupling limit for a Fermi gas in a random potential
    • T. G. Ho, L. J. Landau, and A. J. Wilkins, On the weak coupling limit for a Fermi gas in a random potential, Rev. Math. Phys. 5:209-298 (1993).
    • (1993) Rev. Math. Phys. , vol.5 , pp. 209-298
    • Ho, T.G.1    Landau, L.J.2    Wilkins, A.J.3
  • 22
    • 0030388835 scopus 로고    scopus 로고
    • Transport equations for elastic and other waves in random media
    • J. B. Keller, G. Papanicolaou, and L. Ryzhik, Transport equations for elastic and other waves in random media, Wave Motion 24:327-370 (1996).
    • (1996) Wave Motion , vol.24 , pp. 327-370
    • Keller, J.B.1    Papanicolaou, G.2    Ryzhik, L.3
  • 27
    • 21844517262 scopus 로고
    • Observation of Quantum Particles on a Large Space-Time Scale
    • L. J. Landau, Observation of Quantum Particles on a Large Space-Time Scale, J. Stat. Phys. 77:259-309 (1994).
    • (1994) J. Stat. Phys. , vol.77 , pp. 259-309
    • Landau, L.J.1
  • 28
    • 3543009193 scopus 로고
    • On the generators of Quantum dynamical semigroups
    • G. Lindblad, On the generators of Quantum dynamical semigroups, Comm. Math. Phys. 48:119-130 (1976).
    • (1976) Comm. Math. Phys. , vol.48 , pp. 119-130
    • Lindblad, G.1
  • 32
    • 21844502570 scopus 로고
    • Asymptotic analysis of a scaled wigner equation and quantum scattering
    • F. Nier, Asymptotic Analysis of a scaled Wigner equation and Quantum Scattering, Transp. Theor. Stat. Phys. 24:591-629 (1995).
    • (1995) Transp. Theor. Stat. Phys. , vol.24 , pp. 591-629
    • Nier, F.1
  • 33
    • 0001485147 scopus 로고    scopus 로고
    • A semi-classical picture of quantum scattering
    • F. Nier, A semi-classical picture of quantum scattering, Ann. Sci. Ec. Norm. Sup. Sér. 4 29:149-183 (1996).
    • (1996) Ann. Sci. Ec. Norm. Sup. Sér. 4 , vol.29 , pp. 149-183
    • Nier, F.1
  • 39
    • 0001200202 scopus 로고
    • Derivation of the transport equation for electrons moving through random impurities
    • H. Spohn, Derivation of the transport equation for electrons moving through random impurities, J. Stat. Phys. 17:385-412 (1977).
    • (1977) J. Stat. Phys. , vol.17 , pp. 385-412
    • Spohn, H.1
  • 44
    • 0004098699 scopus 로고
    • P. H. E. Meijer, ed. (Gordon and Breach, New York)
    • R. Zwanzig, Quantum Statistical Mechanics, P. H. E. Meijer, ed. (Gordon and Breach, New York, 1966).
    • (1966) Quantum Statistical Mechanics
    • Zwanzig, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.